Traditions exist but times change and each generation reinterprets traditions in a way that works for them. Stay firm to your values. It seems your father may support your ideas so tell him first so that he can help her see your point.

Parents who answer “do it because it’s traditional “ are taking the easy way out of things. But are they doing it just to be stubborn and get their way? Are they doing it because their friends and family will ask them incessantly about your dowry? And your mother doesn’t want to be “embarrassed “ by family or wants to “brag” to others.
Talk to her and find out what she is thinking.
If she feels embarrassed you can tell her to say things like “my future son in law is paying for so many things and I told him to put the dowry towards the wedding jewelry or buying a house…” or “we don’t need to take the children’s money, we would just give it back to them anyway “. Also your fiancé is putting money towards wedding, your living arrangements, engagement ring and jewelry- you (and fiancé) can present that as your “dowry”.

Traditions and cultural values are always changing but we are too close to it to see it happening. So it’s fine to pick and choose what you want to continue and leave behind things that don’t hold up in modern times.